COMEDK · Maths · 36. Probability

A bag contans $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $\frac{m e a n o f X}{s t a n d a r d d e v i a t i o n o f X}$ is equal to

A $4$
B $4 \sqrt{3}$
C $3 \sqrt{2}$
D $\frac{4 \sqrt{3}}{3}$

Verified Solution

Answer & Solution

Correct Answer

(B) $4 \sqrt{3}$

Step-by-step Solution

Detailed explanation

The total number of balls is $30 + 10 = 40$. The probability of drawing a white ball in a single trial is $p = \dfrac{30}{40} = \dfrac{3}{4}$. The probability of drawing a red ball is $q = 1 - p = 1 - \dfrac{3}{4} = \dfrac{1}{4}$. The number of trials is $n = 16$. Since…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A bag contans 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then mean of Xstandard deviation of X is equal to

Step-by-step Solution

A bag contans $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $\frac{m e a n o f X}{s t a n d a r d d e v i a t i o n o f X}$ is equal to